Bethe’s theory

A most remarkable feature of Bethe s theory, pointed out by Bloch [8], is that p ax is the same in Bohr and Bethe theory, not only in the present, simplified picture but also in the more detailed mathematical form. 

The principal parameter characterizing the molecular stopping power in Bethe s theory is the average ionization potential Im, which depends only on the properties of the molecule. There are different ways of... 

K s> mentioned earlier, these formulations are applicable to structureless particles (bare ions). The only one of them that may be easily extended to complex ions is the perturbative formulation, either in the form of Bethe s theory for atomic targets or Lindhard s theory (dielectric formalism, DF) for the electron gas model. In addition, a comprehensive semiclassical approach, which extends the Bohr model to complex ions, has been developed more recently by Sigmund et al. [26]. 

The main process of energy loss for heavy charged particle occurs via Coulomb interaction with the orbital electron of the stopping material. In order to describe this form of energy loss, two theories were formulated in the 1900s, known as Bohr s and Bethe s theory. Before discussing these formulations in detail, it is important to first present the underlying assumptions inherent in both theories ... 

For low kinetic energies (within region 1 of Fig. 1.1), Bethe s theory fails to adequately describe the variation of because the orbital electrons of the medium... 

Deutsch and Mark compared the classical expression with a theory developed by Bethe.37 Bethe s calculations showed that the ionization cross section for an atomic electron is approximately proportional to the mean square radius of the appropriate n,l electronic shell. Experiment had also shown a correlation between the maximum in the atomic cross section and the sum of the mean square radii of all outer electrons. This led to the replacement of the Bohr radius with the radius of the corresponding subshell the ionization cross section is now given by,... 

I like to emphasize that Fig. 1 is not meant to indicate any fundamental limitation of quantum mechanics both Bohr s and Bethe s formulae invoke mathematical approximations to the underlying physical models, and Bethe s formula in particular relies on first-order perturbation theory for both distant and close collisions. 

One aspect of the eondensed phase regarding the delocalization of the deposited energy has been alluded to in See. 1.3. Here we will eonsider the modifications on the oseillator strength and the mean exeitation potential, due to eondensation, whieh would enter in Bethe s stopping power theory [see Eqs. (4-7)]. 

Crystal field theory has its origins in Hans Bethe s famous 1929 paper Splitting of terms in crystals. In that paper Bethe demonstrated what happens to the various states of an ion when it is placed in a crystalline environment of definite symmetry. Later, John Van Vleck showed that the results of that investigation would apply equally well to a transition-metal compound if it could be approximated as a metal ion surrounded by ligands which only interact electrostatically with the... 

Gordon R (2007) Bethe s aperture theory for arrays. Phys Rev A 76 053806... 

In connexion with the two interesting experimental papers by Rupp and Wierl, I should like to attempt to give a concise outline of the way in which the theoretical treatment of interference phenomena with X-rays and electrons has been developed hitherto. I particularly wish to emphasize those points which eventually led to the adoption of the Darwin-Ewald dispersion theory of X-rays, in order to draw comparisons with the present position in the realm of electrons. This will perhaps make it clear to what extent we are meantime obliged in the case of electrons to accept Bethe s dispersion theory, and which experiments seem best adapted for testing the special results of this theory. 

In 1951, chemists trying to make sense of metal complex optical spectra and color returned to an emphasis on the ionic nature of the coordinate covalent bond. Coordination chemists rediscovered physicists Hans Bethe s and John van Vleck s crystal field theory (CFT),... 

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